Saddle-Reset for Robust Parameter Estimation and Identifiability Analysis of Nonlinear Mixed Effects Models.

Area of Science:

• Pharmacometrics
• Computational Statistics
• Nonlinear Modeling

Background:

• Gradient-based optimization methods, like Broyden-Fletcher-Goldfarb-Shanno (BFGS), are crucial for parameter estimation in nonlinear mixed effects (NLME) models.
• These methods can prematurely terminate, often at saddle points on the likelihood surface, leading to inaccurate parameter estimates.
• Distinguishing between minima, maxima, and saddle points is a known challenge for numerical optimization algorithms.

Purpose of the Study:

• To address the issue of premature termination at saddle points during likelihood maximization in NLME models.
• To propose and validate a novel algorithm, saddle-reset, to improve the reliability of parameter estimation.
• To demonstrate the algorithm's capability in identifying practical parameter non-identifiability.

Main Methods:

• Development of the saddle-reset algorithm, which utilizes the second partial derivative test to identify saddle points.
• Implementation of the saddle-reset algorithm within the NONMEM software (version 7.4 and higher).
• Application of the algorithm to four published pharmacometric models and two specifically designed non-identifiable models.

Main Results:

• The saddle-reset algorithm successfully avoids termination at saddle points during parameter estimation.
• The algorithm effectively identifies instances of practical parameter non-identifiability in NLME models.
• Successful implementation in industry-standard NONMEM software facilitates its practical application.

Conclusions:

• The saddle-reset algorithm offers a robust solution to overcome saddle point termination in NLME parameter estimation.
• This method enhances the accuracy and reliability of parameter estimates, particularly in complex pharmaceutical models.
• The algorithm serves as a valuable tool for uncovering and addressing parameter non-identifiability, improving model interpretability and predictive power.